 Hi and welcome to the session. I am Purva and I will help you with the following question. Find the area between the curves y is equal to x and y is equal to x square. Now the area between the curves y is equal to fx and y is equal to gx where gx is less than equal to fx and x is equal to a and x is equal to b is given by integral limit is from a to b fx minus gx dx where We have b is greater than a in interval a b This is the key idea which we will use to solve this question Now we begin with this solution We have to find the area between the curves y is equal to x and y is equal to x square Now y is equal to x square is a parabola with vertex at origin and symmetric about y axis So we have this parabola y is equal to x square with vertex at origin and this is symmetric about y axis and This y is equal to x is a line which is passing through 00, 11, 22 and so on Now this shaded region is the region whose area is to be found out So to find the area of the shaded region what we do is we drop the line from this point 1 comma 1 down on x-axis and we mark the points a, c, o and b as shown in the figure Therefore we have required area is equal to area of triangle oab minus area of a, c, o, b, a This is equal to Integral now area of triangle oab is given by x dx and Clearly in the figure we can see that the limit is from 0 to 1. So we have limit is from 0 to 1 Minus integral limit is from 0 to 1. Now area of a, c, o, b, a is given by x square dx Now this is equal to integrating x we get x square by 2 and Limit is from 0 to 1 Minus integrating x square we get x cube by 3 and here again limit is from 0 to 1 This is equal to now putting the limits we get 1 by 2 Minus 0 that is upper limit minus lower limit minus again We put the limits we get 1 by 3 minus 0 and this is equal to 1 by 2 minus 1 by 3 now Taking the LCM and subtracting we get this is equal to 1 by 6 Hence the required area is equal to 1 by 6. So this is our required answer. Hope you have understood the solution. Take care and God bless you